Your baby's father can and should support you and your child. Congratulations to you and him on the upcoming birth of your child and to him for wanting to support you. But you do not need to give up the support you receive from your parents for the baby's father to provide additional support. Why make things harder for you and your baby before the baby is even born?
Legally, your parents are required to support you until you are 18 and they can use legal process to try to get you back home if you move out without their permission before you turn 18. In 3 months, you will be a legal adult and then would not need your parents' permission to move out of their home. Why not see how things work out for those additional 3 months?
You may be sorry later, if you need your parents' help but you cut them off and stopped accepting their help while you are still a minor.
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Attorney Rich is right - why not just wait 3 months? Your boyfriend can certainly provide support to you and the baby - both emotionally and financially - while you are still living with your parents. Your parents may give you permission to move in with your boyfriend - have you asked them? Don't burn any bridges with your parents now . . . you will need their support in the coming months and years. Good luck.
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